Exercise 58 Page 212

Both Don and Diego correctly drew the graph of y=x^2-2x-8.

Let's see what the graphs of Don and Diego represent.

Don's Graph

Don shaded a region. This is a graph of an inequality, not a graph of a solution set.

Don's graph illustrates the inequality x^2-2x-8

Diego's Graph

Diego shaded a solution set on the number line based on the correct parabola. Let's check whether this is the correct solution by checking a value in the shaded set.

Let's check x=0.

Since -8 is not greater than 0, Diego shaded the solution set of x^2-2x-8<0. This is not what their goal was, so this is not correct.

The Correct Graph

The correct graph shades the part of the number line that corresponds to the values of x for which the parabola is above the x-axis.